Actual source code: ex8.c

petsc-3.11.4 2019-09-28
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  1: static char help[] = "Time-dependent PDE in 2d for calculating joint PDF. \n";
  2: /*
  3:    p_t = -x_t*p_x -y_t*p_y + f(t)*p_yy
  4:    xmin < x < xmax, ymin < y < ymax;

  6:    Boundary conditions:
  7:    Zero dirichlet in y using ghosted values
  8:    Periodic in x

 10:    Note that x_t and y_t in the above are given functions of x and y; they are not derivatives of x and y. 
 11:    x_t = (y - ws)  
 12:    y_t = (ws/2H)*(Pm - Pmax*sin(x) - D*(w - ws))

 14:    In this example, we can see the effect of a fault, that zeroes the electrical power output
 15:    Pmax*sin(x), on the PDF. The fault on/off times can be controlled by options -tf and -tcl respectively.

 17: */

 19: #include <petscdm.h>
 20: #include <petscdmda.h>
 21: #include <petscts.h>

 23: static const char *const BoundaryTypes[] = {"NONE","GHOSTED","MIRROR","PERIODIC","DMBoundaryType","DM_BOUNDARY_",0};

 25: /*
 26:    User-defined data structures and routines
 27: */
 28: typedef struct {
 29:   PetscScalar ws;   /* Synchronous speed */
 30:   PetscScalar H;    /* Inertia constant */
 31:   PetscScalar D;    /* Damping constant */
 32:   PetscScalar Pmax,Pmax_s; /* Maximum power output of generator */
 33:   PetscScalar PM_min; /* Mean mechanical power input */
 34:   PetscScalar lambda; /* correlation time */
 35:   PetscScalar q;      /* noise strength */
 36:   PetscScalar mux;    /* Initial average angle */
 37:   PetscScalar sigmax; /* Standard deviation of initial angle */
 38:   PetscScalar muy;    /* Average speed */
 39:   PetscScalar sigmay; /* standard deviation of initial speed */
 40:   PetscScalar rho;    /* Cross-correlation coefficient */
 41:   PetscScalar xmin;   /* left boundary of angle */
 42:   PetscScalar xmax;   /* right boundary of angle */
 43:   PetscScalar ymin;   /* bottom boundary of speed */
 44:   PetscScalar ymax;   /* top boundary of speed */
 45:   PetscScalar dx;     /* x step size */
 46:   PetscScalar dy;     /* y step size */
 47:   PetscScalar disper_coe; /* Dispersion coefficient */
 48:   DM          da;
 49:   PetscInt    st_width; /* Stencil width */
 50:   DMBoundaryType bx; /* x boundary type */
 51:   DMBoundaryType by; /* y boundary type */
 52:   PetscReal        tf,tcl; /* Fault incidence and clearing times */
 53: } AppCtx;

 55: PetscErrorCode Parameter_settings(AppCtx*);
 56: PetscErrorCode ini_bou(Vec,AppCtx*);
 57: PetscErrorCode IFunction(TS,PetscReal,Vec,Vec,Vec,void*);
 58: PetscErrorCode IJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*);
 59: PetscErrorCode PostStep(TS);

 61: int main(int argc, char **argv)
 62: {
 64:   Vec            x;  /* Solution vector */
 65:   TS             ts;   /* Time-stepping context */
 66:   AppCtx         user; /* Application context */
 67:   PetscViewer    viewer;

 69:   PetscInitialize(&argc,&argv,"petscopt_ex8", help);if (ierr) return ierr;

 71:   /* Get physics and time parameters */
 72:   Parameter_settings(&user);
 73:   /* Create a 2D DA with dof = 1 */
 74:   DMDACreate2d(PETSC_COMM_WORLD,user.bx,user.by,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,user.st_width,NULL,NULL,&user.da);
 75:   DMSetFromOptions(user.da);
 76:   DMSetUp(user.da);
 77:   /* Set x and y coordinates */
 78:   DMDASetUniformCoordinates(user.da,user.xmin,user.xmax,user.ymin,user.ymax,0,0);
 79:   DMDASetCoordinateName(user.da,0,"X - the angle");
 80:   DMDASetCoordinateName(user.da,1,"Y - the speed");

 82:   /* Get global vector x from DM  */
 83:   DMCreateGlobalVector(user.da,&x);

 85:   ini_bou(x,&user);
 86:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"ini_x",FILE_MODE_WRITE,&viewer);
 87:   VecView(x,viewer);
 88:   PetscViewerDestroy(&viewer);

 90:   TSCreate(PETSC_COMM_WORLD,&ts);
 91:   TSSetDM(ts,user.da);
 92:   TSSetProblemType(ts,TS_NONLINEAR);
 93:   TSSetType(ts,TSARKIMEX);
 94:   TSSetIFunction(ts,NULL,IFunction,&user);
 95:   /*  TSSetIJacobian(ts,NULL,NULL,IJacobian,&user); */
 96:   TSSetApplicationContext(ts,&user);
 97:   TSSetTimeStep(ts,.005);
 98:   TSSetFromOptions(ts);
 99:   TSSetPostStep(ts,PostStep);
100:   TSSolve(ts,x);

102:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"fin_x",FILE_MODE_WRITE,&viewer);
103:   VecView(x,viewer);
104:   PetscViewerDestroy(&viewer);

106:   VecDestroy(&x);
107:   DMDestroy(&user.da);
108:   TSDestroy(&ts);
109:   PetscFinalize();
110:   return ierr;
111: }

113: PetscErrorCode PostStep(TS ts)
114: {
116:   Vec            X;
117:   AppCtx         *user;
118:   PetscReal      t;
119:   PetscScalar    asum;

122:   TSGetApplicationContext(ts,&user);
123:   TSGetTime(ts,&t);
124:   TSGetSolution(ts,&X);
125:   /*
126:   if (t >= .2) {
127:     TSGetSolution(ts,&X);
128:     VecView(X,PETSC_VIEWER_BINARY_WORLD);
129:     exit(0);
130:      results in initial conditions after fault in binaryoutput
131:   }*/

133:   if ((t > user->tf) && (t < user->tcl)) user->Pmax = 0.0; /* A short-circuit that drives the electrical power output (Pmax*sin(delta)) to zero */
134:   else user->Pmax = user->Pmax_s;

136:   VecSum(X,&asum);
137:   PetscPrintf(PETSC_COMM_WORLD,"sum(p) at t = %f = %f\n",(double)t,(double)(asum));
138:   return(0);
139: }

141: PetscErrorCode ini_bou(Vec X,AppCtx* user)
142: {
144:   DM             cda;
145:   DMDACoor2d     **coors;
146:   PetscScalar    **p;
147:   Vec            gc;
148:   PetscInt       M,N,Ir,J;
149:   PetscMPIInt    rank;

152:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
153:   DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
154:   user->dx = (user->xmax - user->xmin)/(M-1); user->dy = (user->ymax - user->ymin)/(N-1);
155:   DMGetCoordinateDM(user->da,&cda);
156:   DMGetCoordinates(user->da,&gc);
157:   DMDAVecGetArrayRead(cda,gc,&coors);
158:   DMDAVecGetArray(user->da,X,&p);

160:   /* Point mass at (mux,muy) */
161:   PetscPrintf(PETSC_COMM_WORLD,"Original user->mux = %f, user->muy = %f\n",user->mux,user->muy);
162:   DMDAGetLogicalCoordinate(user->da,user->mux,user->muy,0.0,&Ir,&J,NULL,&user->mux,&user->muy,NULL);
163:   user->PM_min = user->Pmax*PetscSinScalar(user->mux);
164:   PetscPrintf(PETSC_COMM_WORLD,"Corrected user->mux = %f, user->muy = %f user->PM_min = %f,user->dx = %f\n",user->mux,user->muy,user->PM_min,user->dx);
165:   if (Ir > -1 && J > -1) {
166:     p[J][Ir] = 1.0;
167:   }

169:   DMDAVecRestoreArrayRead(cda,gc,&coors);
170:   DMDAVecRestoreArray(user->da,X,&p);
171:   return(0);
172: }

174: /* First advection term */
175: PetscErrorCode adv1(PetscScalar **p,PetscScalar y,PetscInt i,PetscInt j,PetscInt M,PetscScalar *p1,AppCtx *user)
176: {
177:   PetscScalar f,fpos,fneg;
179:   f   =  (y - user->ws);
180:   fpos = PetscMax(f,0);
181:   fneg = PetscMin(f,0);
182:   if (user->st_width == 1) {
183:     *p1 = fpos*(p[j][i] - p[j][i-1])/user->dx + fneg*(p[j][i+1] - p[j][i])/user->dx;
184:   } else if (user->st_width == 2) {
185:     *p1 = fpos*(3*p[j][i] - 4*p[j][i-1] + p[j][i-2])/(2*user->dx) + fneg*(-p[j][i+2] + 4*p[j][i+1] - 3*p[j][i])/(2*user->dx);
186:   } else if (user->st_width == 3) {
187:     *p1 = fpos*(2*p[j][i+1] + 3*p[j][i] - 6*p[j][i-1] + p[j][i-2])/(6*user->dx) + fneg*(-p[j][i+2] + 6*p[j][i+1] - 3*p[j][i] - 2*p[j][i-1])/(6*user->dx);
188:   }
189:   /* *p1 = f*(p[j][i+1] - p[j][i-1])/user->dx;*/
190:   return(0);
191: }

193: /* Second advection term */
194: PetscErrorCode adv2(PetscScalar **p,PetscScalar x,PetscScalar y,PetscInt i,PetscInt j,PetscInt N,PetscScalar *p2,AppCtx *user)
195: {
196:   PetscScalar f,fpos,fneg;
198:   f   = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(x) - user->D*(y - user->ws));
199:   fpos = PetscMax(f,0);
200:   fneg = PetscMin(f,0);
201:   if (user->st_width == 1) {
202:     *p2 = fpos*(p[j][i] - p[j-1][i])/user->dy + fneg*(p[j+1][i] - p[j][i])/user->dy;
203:   } else if (user->st_width ==2) {
204:     *p2 = fpos*(3*p[j][i] - 4*p[j-1][i] + p[j-2][i])/(2*user->dy) + fneg*(-p[j+2][i] + 4*p[j+1][i] - 3*p[j][i])/(2*user->dy);
205:   } else if (user->st_width == 3) {
206:     *p2 = fpos*(2*p[j+1][i] + 3*p[j][i] - 6*p[j-1][i] + p[j-2][i])/(6*user->dy) + fneg*(-p[j+2][i] + 6*p[j+1][i] - 3*p[j][i] - 2*p[j-1][i])/(6*user->dy);
207:   }

209:   /* *p2 = f*(p[j+1][i] - p[j-1][i])/user->dy;*/
210:   return(0);
211: }

213: /* Diffusion term */
214: PetscErrorCode diffuse(PetscScalar **p,PetscInt i,PetscInt j,PetscReal t,PetscScalar *p_diff,AppCtx * user)
215: {
217:   if (user->st_width == 1) {
218:     *p_diff = user->disper_coe*((p[j-1][i] - 2*p[j][i] + p[j+1][i])/(user->dy*user->dy));
219:   } else if (user->st_width == 2) {
220:     *p_diff = user->disper_coe*((-p[j-2][i] + 16*p[j-1][i] - 30*p[j][i] + 16*p[j+1][i] - p[j+2][i])/(12.0*user->dy*user->dy));
221:   } else if (user->st_width == 3) {
222:     *p_diff = user->disper_coe*((2*p[j-3][i] - 27*p[j-2][i] + 270*p[j-1][i] - 490*p[j][i] + 270*p[j+1][i] - 27*p[j+2][i] + 2*p[j+3][i])/(180.0*user->dy*user->dy));
223:   }
224:   return(0);
225: }

227: PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
228: {
230:   AppCtx         *user=(AppCtx*)ctx;
231:   DM             cda;
232:   DMDACoor2d     **coors;
233:   PetscScalar    **p,**f,**pdot;
234:   PetscInt       i,j;
235:   PetscInt       xs,ys,xm,ym,M,N;
236:   Vec            localX,gc,localXdot;
237:   PetscScalar    p_adv1 = 0.0,p_adv2 = 0.0,p_diff = 0;
238:   PetscScalar    diffuse1,gamma;

241:   DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
242:   DMGetCoordinateDM(user->da,&cda);
243:   DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);

245:   DMGetLocalVector(user->da,&localX);
246:   DMGetLocalVector(user->da,&localXdot);

248:   DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
249:   DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
250:   DMGlobalToLocalBegin(user->da,Xdot,INSERT_VALUES,localXdot);
251:   DMGlobalToLocalEnd(user->da,Xdot,INSERT_VALUES,localXdot);

253:   DMGetCoordinatesLocal(user->da,&gc);

255:   DMDAVecGetArrayRead(cda,gc,&coors);
256:   DMDAVecGetArrayRead(user->da,localX,&p);
257:   DMDAVecGetArrayRead(user->da,localXdot,&pdot);
258:   DMDAVecGetArray(user->da,F,&f);

260:   gamma = user->D*user->ws/(2*user->H);
261:   diffuse1 = user->lambda*user->lambda*user->q/(user->lambda*gamma+1)*(1.0 - PetscExpScalar(-t*(gamma+1.0)/user->lambda));
262:   user->disper_coe = user->ws*user->ws/(4*user->H*user->H)*diffuse1;

264:   for (i=xs; i < xs+xm; i++) {
265:     for (j=ys; j < ys+ym; j++) {
266:       adv1(p,coors[j][i].y,i,j,M,&p_adv1,user);
267:       adv2(p,coors[j][i].x,coors[j][i].y,i,j,N,&p_adv2,user);
268:       diffuse(p,i,j,t,&p_diff,user);
269:       f[j][i] = -p_adv1 - p_adv2  + p_diff - pdot[j][i];
270:     }
271:   }
272:   DMDAVecRestoreArrayRead(user->da,localX,&p);
273:   DMDAVecRestoreArrayRead(user->da,localX,&pdot);
274:   DMRestoreLocalVector(user->da,&localX);
275:   DMRestoreLocalVector(user->da,&localXdot);
276:   DMDAVecRestoreArray(user->da,F,&f);
277:   DMDAVecRestoreArrayRead(cda,gc,&coors);

279:   return(0);
280: }

282: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat J,Mat Jpre,void *ctx)
283: {
285:   AppCtx         *user=(AppCtx*)ctx;
286:   DM             cda;
287:   DMDACoor2d     **coors;
288:   PetscInt       i,j;
289:   PetscInt       xs,ys,xm,ym,M,N;
290:   Vec            gc;
291:   PetscScalar    val[5],xi,yi;
292:   MatStencil     row,col[5];
293:   PetscScalar    c1,c3,c5,c1pos,c1neg,c3pos,c3neg;

296:   DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
297:   DMGetCoordinateDM(user->da,&cda);
298:   DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);

300:   DMGetCoordinatesLocal(user->da,&gc);
301:   DMDAVecGetArrayRead(cda,gc,&coors);
302:   for (i=xs; i < xs+xm; i++) {
303:     for (j=ys; j < ys+ym; j++) {
304:       PetscInt nc = 0;
305:       xi = coors[j][i].x; yi = coors[j][i].y;
306:       row.i = i; row.j = j;
307:       c1        = (yi-user->ws)/user->dx;
308:       c1pos    = PetscMax(c1,0);
309:       c1neg    = PetscMin(c1,0);
310:       c3        = (user->ws/(2.0*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(xi) - user->D*(yi - user->ws))/user->dy;
311:       c3pos    = PetscMax(c3,0);
312:       c3neg    = PetscMin(c3,0);
313:       c5        = (PetscPowScalar((user->lambda*user->ws)/(2*user->H),2)*user->q*(1.0-PetscExpScalar(-t/user->lambda)))/(user->dy*user->dy);
314:       col[nc].i = i-1; col[nc].j = j;   val[nc++] = c1pos;
315:       col[nc].i = i+1; col[nc].j = j;   val[nc++] = -c1neg;
316:       col[nc].i = i;   col[nc].j = j-1; val[nc++] = c3pos + c5;
317:       col[nc].i = i;   col[nc].j = j+1; val[nc++] = -c3neg + c5;
318:       col[nc].i = i;   col[nc].j = j;   val[nc++] = -c1pos + c1neg -c3pos + c3neg -2*c5 -a;
319:       MatSetValuesStencil(Jpre,1,&row,nc,col,val,INSERT_VALUES);
320:     }
321:   }
322:   DMDAVecRestoreArrayRead(cda,gc,&coors);

324:    MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
325:   MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
326:   if (J != Jpre) {
327:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
328:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
329:   }
330:   return(0);
331: }

333: PetscErrorCode Parameter_settings(AppCtx *user)
334: {
336:   PetscBool      flg;


340:   /* Set default parameters */
341:   user->ws     = 1.0;
342:   user->H      = 5.0;
343:   user->D      = 0.0;
344:   user->Pmax = user->Pmax_s  = 2.1;
345:   user->PM_min = 1.0;
346:   user->lambda = 0.1;
347:   user->q      = 1.0;
348:   user->mux    = PetscAsinScalar(user->PM_min/user->Pmax);
349:   user->sigmax = 0.1;
350:   user->sigmay = 0.1;
351:   user->rho    = 0.0;
352:   user->xmin   = -PETSC_PI;
353:   user->xmax   = PETSC_PI;
354:   user->bx     = DM_BOUNDARY_PERIODIC;
355:   user->by     = DM_BOUNDARY_GHOSTED;
356:   user->tf = user->tcl = -1;
357:   user->ymin   = -2.0;
358:   user->ymax   = 2.0;
359:   user->st_width = 1;

361:   PetscOptionsGetScalar(NULL,NULL,"-ws",&user->ws,&flg);
362:   PetscOptionsGetScalar(NULL,NULL,"-Inertia",&user->H,&flg);
363:   PetscOptionsGetScalar(NULL,NULL,"-D",&user->D,&flg);
364:   PetscOptionsGetScalar(NULL,NULL,"-Pmax",&user->Pmax,&flg);
365:   PetscOptionsGetScalar(NULL,NULL,"-PM_min",&user->PM_min,&flg);
366:   PetscOptionsGetScalar(NULL,NULL,"-lambda",&user->lambda,&flg);
367:   PetscOptionsGetScalar(NULL,NULL,"-q",&user->q,&flg);
368:   PetscOptionsGetScalar(NULL,NULL,"-mux",&user->mux,&flg);
369:   PetscOptionsGetScalar(NULL,NULL,"-muy",&user->muy,&flg);
370:   if (flg == 0) {
371:     user->muy = user->ws;
372:   }
373:   PetscOptionsGetScalar(NULL,NULL,"-xmin",&user->xmin,&flg);
374:   PetscOptionsGetScalar(NULL,NULL,"-xmax",&user->xmax,&flg);
375:   PetscOptionsGetScalar(NULL,NULL,"-ymin",&user->ymin,&flg);
376:   PetscOptionsGetScalar(NULL,NULL,"-ymax",&user->ymax,&flg);
377:   PetscOptionsGetInt(NULL,NULL,"-stencil_width",&user->st_width,&flg);
378:   PetscOptionsGetEnum(NULL,NULL,"-bx",BoundaryTypes,(PetscEnum*)&user->bx,&flg);
379:   PetscOptionsGetEnum(NULL,NULL,"-by",BoundaryTypes,(PetscEnum*)&user->by,&flg);
380:   PetscOptionsGetReal(NULL,NULL,"-tf",&user->tf,&flg);
381:   PetscOptionsGetReal(NULL,NULL,"-tcl",&user->tcl,&flg);
382:   return(0);
383: }

385: /*TEST

387:    build:
388:       requires: !complex x

390:    test:
391:       args: -ts_max_steps 1
392:       localrunfiles: petscopt_ex8
393:       timeoutfactor: 3

395: TEST*/